1. Dmitri Lokshtanov Norsk Hydro Research Centre, Bergen.
Suppression of multiples from complex sea-floor by a wave-equation approach
Dmitri Lokshtanov
Norsk Hydro Research Centre, Bergen.

2. Outline Main features of WE approach
Suppression of water-layer multiples and peg-legs
Prediction of water-layer multiples and peg-legs
Conclusions

3. WE approach - the main features
Suppresses water-layer multiples and peg-legs. Requires approximate knowledge of the water-bottom geometry.
The predicted multiples are split into three terms. Each term contains multiple events which require the same amplitude correction. All multiples of all orders are suppressed simultaneously in one consistent step (in one or a few time windows).
The prediction of multiples is performed in the same domain as used for multiple suppression. Both multiple reflections and diffractions are predicted.

5. Subtraction of water-layer multiples - 1

6. The operator Pg transforms the primary reflection event recorded at receiver 1 into the multiple event recorded at receiver 2 (Wiggins, 1988; Berryhill & Kim, 1986).
The operator Pg transforms the primary reflection event recorded at receiver 1 into the multiple event recorded at receiver 2 (Wiggins, 1988; Berryhill & Kim, 1986).

7. Subtraction of water-layer multiples - 2

8. Two approaches for multiple prediction
Simple ‘locally’ 1D sea-floor; arbitrary 2D structure below it. The procedure starts from the Radon transformed CMP gathers
Complex sea-floor; arbitrary 2D structure below it. The procedure starts from the Radon transformed CS gathers.

9. Stack before multiple suppression Stack after WE multiple suppression
 T. Shetland
 T. Draupne
 T. Brent
Stack before multiple suppression Stack after WE multiple suppression

10. Constant P sections (angle at the surface is about 10º)
Input After WE multiple suppression

11. Stack before multiple suppression (left) and after WE multiple suppression (right).
The pink line shows the expected position of the first-order water-layer peg-leg from the
Top Cretaceous (black line). The multiple period is about 140 msec.

12. Constant P sections (angle at the surface is about 8º)
Input After WE multiple suppression Difference

13. Prediction of multiples from the receiver side for irregular sea-floor

14. Prediction of multiples from the source side for irregular sea-floor

15. Velocity model for FD modelling (with ProMax)

16. Input P-section (zero angle) Receiver-side prediction

17. Input P-section (zero angle) Receiver-side prediction

18. Input P-section (zero angle) After prediction + subtraction

19. Input P-section (angle 20 degrees) Receiver-side prediction

20. Input P-section (20 degrees) Receiver-side prediction Source-side prediction

21. Input P-section (20 degrees) After prediction + subtraction

22. Input CS gather After prediction + subtraction

23. Input CS gather After prediction + subtraction

24. Stack before multiple suppression

25. Stack after multiple suppression

26. Stack before multiple suppression Stack after multiple suppression

27. Input NMO gathers NMO gathers after WE + VF

28. Recent papers on WE approach
Jiao J., Leger P. and Stevens J, 2002, Enhancements to wave-equation multiple attenuation, 72nd SEG Meeting, Expanded Abstracts.
Hill R., Langan R., Nemeth T., Zhao M. and Bube K., 2002, Beam methods for predictive suppression of seismic multiples in deep water, 72nd SEG Meeting, Expanded Abstracts.
Hugonnet P., 2002, Partial surface related multiple elimination, 72nd SEG Meeting, Expanded Abstracts.

29. Conclusions
WE approach – performs well if the main free-surface multiples are water-layer multiples and peg-legs and if the structural variations in the crossline direction are not severe
Both multiple reflections and multiple diffractions are accounted for. All predicted multiples of all orders are suppressed simultaneously in one consistent step
The prediction of multiples is performed in the same domain as used for multiple suppression

30. Acknowledgements
Many thanks to Norsk Hydro and CREWES for one year of freedom in a fantastic country – Canada !
Thanks to Norsk Hydro for permission to present the paper.